Power distribution systems deliver electric powers from distributed generators and transmission systems to power consumers. The distribution system may be either a 3-phase 4 wire system, or a 3-phase 3 wire system. The power from the transmission system or the generators is delivered to the consumers through transmission lines, and various voltage regulation devices, such as shunt capacitors, step voltage regulators, and transformers. The consumer loads may be single phase, two-phase or three-phase. The loads may be constant power load, constant current load, or constant impedance load.
FIG. 1 shows schematic diagrams of a sample distribution system including both the three-phase representation 101 and one-line diagram 102. The sample system includes one grounded Wye-connected three-phase source 110, two three-phase transmission lines 120 and 140, one grounded Wye-connected three-phase load 150, and one three-phase transformer 130 with Delta/Grounded Wye connection. There are four three-phase buses in the system, including bus 115, bus 125, bus 135 and bus 145.
The purpose of three-phase power flow analysis is to obtain the voltages at each phase of any bus in the power distribution system, for specified source and load conditions. After the voltages are known, currents and powers in each branch on each phase, as well as the output of the generation sources, can be determined analytically.
The effectiveness of power flow methods are depended on what type of devices is modeled, and how the device is connected within itself and with other devices. The grounded Wye, and Delta are commonly used for the distribution loads, distributed sources or shunt capacitors. The typical connection type of transformer or voltage regulator windings includes grounded Wye, ungrounded Wye, and Delta.
Depending on known parameters, buses of the distribution system can be classified as (1) a swing bus, if the voltage magnitude |V| and the phase angle θ are known; (2) as a PQ bus, if the active power P and the reactive power Q are known; and (3) as a PV bus, if the active power P and voltage magnitude |V| are known. The bus type is determined by the known parameters of connected sources and loads.
Various methods for solving three phase power flow problem are known. Those methods differ in either the form of the equation describing the system, or the numerical techniques used, and usually are either topology based or matrix based. Typical topology based methods include backward/forward sweep method, and ladder method. Typical matrix based methods include implicit Z-bus matrix method, Newton-Raphson method, and Fast Decoupled method. All of those methods have their own limitations when applied to large systems either in modeling capabilities or computational efficiency. The computational efficiency is a major challenges for the admittance matrix methods.